GPs are used to regress force over position for each mode \(n\) , based on a dataset of measured pose and force \(\mathcal {D} = \left\lbrace \left\lbrace \mathbf {x}_1,\mathbf {f}_1\right\rbrace \dots ,\left\lbrace \mathbf {x}_M,\mathbf {f}_M\right\rbrace \right\rbrace \) . We fit a GP Model [1]} that gives a Gaussian variable \(\hat{\mathbf {f}}(\mathbf {x})\sim \mathcal {N}(\mathbf {\mu }_f(\mathbf {x}), \mathbf {\Sigma }_f(\mathbf {x}))\)  for a pose \(\mathbf {x}\) , given a mean function \(\mathbf {m}(\mathbf {x}) \in \mathbb {R}^6\) , kernel function \(k(\mathbf {x},\mathbf {x}^{\prime })\in \mathbb {R}\) , and observed data \(\mathcal {D}\) . The GP models for each dimension of \(\mathbf {f}\)  are fit independently and the covariance \(\mathbf {\Sigma }_f\)  is therefore diagonal. In the sequel, we consider the fitting of a single dimension of \(\mathbf {f}\)  with corresponding scalars \(f\) , \(\mu _f\) , \(\Sigma _f\) .
